这与我之前提到的三次贝塞尔曲线类似。我有一个起始点,一个终点和一个应该位于二次贝塞尔曲线上的点。给定这三个点,我想要在WPF中绘制一个二次贝塞尔曲线段,但我需要单个控制点值(在二次贝塞尔曲线段中为Point1)才能绘制它。是否有一种计算或方法可以确定该值并因此绘制我的二次贝塞尔曲线?谢谢!
最佳二次拟合比最佳三次拟合要简单。以下是一些代码:
static class DrawingUtility
{
static void bez3pts1(double x0, double y0, double x3, double y3, double x2, double y2, out double x1, out double y1)
{
// find chord lengths
double c1 = Math.Sqrt((x3 - x0) * (x3 - x0) + (y3 - y0) * (y3 - y0));
double c2 = Math.Sqrt((x3 - x2) * (x3 - x2) + (y3 - y2) * (y3 - y2));
// guess "best" t
double t = c1 / (c1 + c2);
// quadratic Bezier is B(t) = (1-t)^2*P0 + 2*t*(1-t)*P1 + t^2*P2
// solving gives P1 = [B(t) - (1-t)^2*P0 - t^2*P2] / [2*t*(1-t)] where P3 is B(t)
x1 = (x3 - (1 - t) * (1 - t) * x0 - t * t * x2) / (2 * t * (1 - t));
y1 = (y3 - (1 - t) * (1 - t) * y0 - t * t * y2) / (2 * t * (1 - t));
}
// pass in a PathFigure and it will append a QuadraticBezierSegment connecting the previous point to int1 and endPt
static public void QuadraticBezierFromIntersection(PathFigure path, Point startPt, Point int1, Point endPt)
{
double x1, y1;
bez3pts1(startPt.X, startPt.Y, int1.X, int1.Y, endPt.X, endPt.Y, out x1, out y1);
path.Segments.Add(new QuadraticBezierSegment { Point1 = new Point(x1, y1), Point2 = endPt } );
}
}